Answer: 121.5 square cm
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Step-by-step explanation
For now we'll focus on triangle MQN.
This is a right triangle with...
- a = MQ = unknown leg
- b = QN = 18 = the other leg
- c = MN = 30 = hypotenuse
Let's use the pythagorean theorem to find the length of MQ.
a^2 + b^2 = c^2
a^2 + 18^2 = 30^2
a^2 = 30^2 - 18^2
a^2 = 576
a = sqrt(576)
a = 24
Side MQ is 24 units long.
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Now let x = length of segment QP.
Because we have 3 similar right triangles, we can form this proportion
MQ/QN = QN/QP
Let's use that to solve for x.
MQ/QN = QN/QP
24/18= 18/x
24x = 18*18
24x = 324
x = 324/24
x = 27/2
x = 13.5
Side QP is 13.5 units long.
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Turn your attention to triangle NQP.
base = QP = 13.5
height = QN = 18
area = 0.5*base*height
area = 0.5*QP*QN
area = 0.5*13.5*18
area = 121.5 square cm